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Psi function can refer, in mathematics, to the ordinal collapsing function ...
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
An elegant and intuitive way to formulate Maxwell's equations is to use complex line bundles or a principal U(1)-bundle, on the fibers of which U(1) acts regularly. The principal U(1)- connection ∇ on the line bundle has a curvature F = ∇ 2 , which is a two-form that automatically satisfies d F = 0 and can be interpreted as a field strength.
The solutions to are multi-component spinor fields, and each component satisfies . A remarkable result of spinor solutions is that half of the components describe a particle while the other half describe an antiparticle; in this case the electron and positron. The Dirac equation is now known to apply for all massive spin- 1 / 2 fermions ...
The Euler equations can be generalized to any simple Lie algebra. [1] The original Euler equations come from fixing the Lie algebra to be s o ( 3 ) {\displaystyle {\mathfrak {so}}(3)} , with generators t 1 , t 2 , t 3 {\displaystyle {t_{1},t_{2},t_{3}}} satisfying the relation [ t a , t b ] = ϵ a b c t c {\displaystyle [t_{a},t_{b}]=\epsilon ...
Euler's second law states that the rate of change of angular momentum L about a point that is fixed in an inertial reference frame (often the center of mass of the body), is equal to the sum of the external moments of force acting on that body M about that point: [1] [4] [5]
Since linear motion is a motion in a single dimension, the distance traveled by an object in particular direction is the same as displacement. [4] The SI unit of displacement is the metre . [ 5 ] [ 6 ] If x 1 {\displaystyle x_{1}} is the initial position of an object and x 2 {\displaystyle x_{2}} is the final position, then mathematically the ...
Dynamic pressure is one of the terms of Bernoulli's equation, which can be derived from the conservation of energy for a fluid in motion. [1] At a stagnation point the dynamic pressure is equal to the difference between the stagnation pressure and the static pressure, so the dynamic pressure in a flow field can be measured at a stagnation point ...
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